5,982 research outputs found
Multi-resolution two-sample comparison through the divide-merge Markov tree
We introduce a probabilistic framework for two-sample comparison based on a
nonparametric process taking the form of a Markov model that transitions
between a "divide" and a "merge" state on a multi-resolution partition tree of
the sample space. Multi-scale two-sample comparison is achieved through
inferring the underlying state of the process along the partition tree. The
Markov design allows the process to incorporate spatial clustering of
differential structures, which is commonly observed in two-sample problems but
ignored by existing methods. Inference is carried out under the Bayesian
paradigm through recursive propagation algorithms. We demonstrate the work of
our method through simulated data and a real flow cytometry data set, and show
that it substantially outperforms other state-of-the-art two-sample tests in
several settings.Comment: Corrected typos. Added Software sectio
The integrated periodogram of a dependent extremal event sequence
We investigate the asymptotic properties of the integrated periodogram
calculated from a sequence of indicator functions of dependent extremal events.
An event in Euclidean space is extreme if it occurs far away from the origin.
We use a regular variation condition on the underlying stationary sequence to
make these notions precise. Our main result is a functional central limit
theorem for the integrated periodogram of the indicator functions of dependent
extremal events. The limiting process is a continuous Gaussian process whose
covari- ance structure is in general unfamiliar, but in the iid case a Brownian
bridge appears. In the general case, we propose a stationary bootstrap
procedure for approximating the distribution of the limiting process. The
developed theory can be used to construct classical goodness-of-fit tests such
as the Grenander- Rosenblatt and Cram\'{e}r-von Mises tests which are based
only on the extremes in the sample. We apply the test statistics to simulated
and real-life data
Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes
A continuous time random walk (CTRW) is a random walk in which both spatial
changes represented by jumps and waiting times between the jumps are random.
The CTRW is coupled if a jump and its preceding or following waiting time are
dependent random variables, respectively. The aim of this paper is to explain
the occurrence of different limit processes for CTRWs with forward- or
backward-coupling in Straka and Henry (2011) using marked point processes. We
also establish a series representation for the different limits. The methods
used also allow us to solve an open problem concerning residual order
statistics by LePage (1981).Comment: revised version, to appear in: Stoch. Process. App
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